Research On The Algorithm Of D(β)-vertex Sum Distinguishing Edge Coloring And Edge Magic Sum Labeling Of Random Graphs

Graph theory has a lot of applications in the field of computer research.The coloring and labeling of graphs have always been an important and active topic in graph theory research.Graph coloring problem was born in the famous "four-color problem" put forward by Kelly.Graph coloring has a wide range of applications in real life,such as map coloring,seat arrangement in examination room,timetable arrangement,transportation,logistics,dangerous goods storage and freight forwarder problem.Abstract the problems in real life as graph coloring problems,through the research and analysis of dyeing theory knowledge,use reasonable methods to solve related problems.There are many kinds of graph coloring,among which the most popular ones are distinguishing edge(total)coloring,chromatic sum edge(total)coloring,reducible edge(total)coloring and D(β)edge(total)coloring.In the published literature on coloring,most of graphs are dyed by traditional methods.Most of these methods can only study the classes of graphs whose graph structure can be described by one or several parameters,and there is no effective method to study the random graphs whose graph topological structure cannot be described by several parameters.In order to solve the coloring problem of vertexs sum distinguishing edges of random graphs,the dissertation designs a coloring algorithm by using objective function and combination number.The algorithm is used to process graph data set,so as to obtain the color and edge coloring results of random graphs within 10 vertexs and special graphs within 16 vertexs.Through the analysis of the coloring results,the related theorems of color and edge coloring of random graphs and special graphs are obtained,and the corresponding conjectures are put forward.It is difficult to get the coloring in a short time because of the large random graph set,so we select part of the graph set to study,so as to verify the correctness of the conjecture.Edge-magic total labelling of graph is a kind of icon number,which means that the sum of labels of any edge and its associated vertex in graph G(p,q)is constant,and all label values of vertex and edge are mapped to set {1,2,…,p+q}.Based on the analysis of the existing research results of magic total labelling,the dissertation designs an edge-magic total labelling decision algorithm,which optimizes the traditional labelling solution space,so as to improve the performance and operation efficiency of the computer.In this dissertation,a judge algorithm is designed to get all edge-magic total labelling of bicyclic graphs within 15 vertices,Through the analysis of the results,finding the rules of edgemagic total labelling for two kinds of composition graphs,and defining the new graph operational symbols to describe such graphs,and finally several theorems are summarized and proved.It is further conjectured that the relevant conclusions are still valid when the vertex number p≥16.